What can you do?
It's a hard problem at it's core. I think most people go through many stages where they realize that people (and themselves) can be wonderful in some regards and horrible in others. To some extent, every action or belief you hold can and will effect the other areas of your life. But there are people everywhere who are deeply flawed but yet are good at something: the great school teacher who is an alcoholic with DUIs, the affable friend who is full of jealousy in love, or in your case, the neighbor who is great to get along with - unless you're Serbian.
So you are faced with a choice: do you shut these people out of your life based on a principle? You can if you want. But you're connected with them. So it's an uneasy compromise. You'll have to accept the good with the bad. You can attempt to reform them, which I already stated will be a difficult process. But if they are really worth that much for you, then you'll do it. And you will face probable failure, unless you have a particularly well developed social skill set.
Otherwise, you can do your best to try to bring out the good and ignore the bad. Of course, you'll be letting the principle slip away here, but it will probably work, at least for a little while. People do this all the time. They turn an eye to the bad. But then you'll grow tired of compromising your beliefs.
I recommend you don't turn a blind eye to it. Don't ignore it. Instead, understand it. Pay attention. What is it, really, that is causing them to believe this? Break down the puzzle and figure it out. After you've figured it out, then you move from there.
From there, you decide if you want to keep them as a friend or not. In my opinion, simply because you had (or have) an attachment to someone doesn't mean they should continue to stay in your life. Maybe you'll decide to try and reform them first, and if you succeed, you kept a friend. Otherwise, you'll either end up awkwardly dissatisfied by staying with them or lonely by yourself for the time being.*
*This is all my opinion. The above is a rather dichotomous way of looking at things. You could say that it is a false dichotomy. Indeed, I'm quite sure there are other ways of viewing this situation and there are a variety of possible end scenarios. That said, I present this argument to try to distill the viewpoints into a simple format which emphasizes both choice and personal responsibility.
My end goal was to try and spur action, not rumination.